Objective: Find C28

-derived molecular solids which are potential

high-Tc superconductors.

†. Figure data taken from N. Breda et al., PRB 62, 130 (2000) and references therein‡. V. H. Crespi, PRB 60, 100 (1999).

Motivation: Recall that Tc~ exp(-1/λ ), and λ =N(0)V

ep for

molecular solids.

Motivation and Objective

Hyperdiamond Solids

V ep=∑

1

M 2

1

g 2∑i , j

g

∣⟨i∣⋅∇V∣ j ⟩∣2

How to make a fullerene superconductor?

Alkali doping of face-bonded C28

H4 HD

Tc for Solid Na@C

28H

4

Covalent vs. Molecular Solid

Structural and Electronic Properties

Band Structure and DOS: C60

vs. C28

H4

Smaller fullerenes have a larger electron phonon interaction potential:† V

ep ∝ curvature‡

In the spirit of C60

:

Step 1: Choose a small fullerene with a large Vep

. Try to do

better than C60

.

→ Next most abundant fullerenes are C36

† and C28

.

Step 2: Make a molecular solid with weakly broadened bands resulting in a large DOS at the band edges.→ Need a close-shell molecule with a large gap, C

24B

4, C

24N

4,

C28

H4, and then find a solid that weakly interacting solid..

Step 3: Electron-dope the conduction band within a rigid band donor picture picture.→ Intercalate alkali atoms into solid.† M. Cote et. al, Phys. Rev. Lett. 81, 697 (1988).

molecule apex-bonded HD face-bonded HD

C24B4 molecules break apart molecules break apart

C24N4 covalent solid hybridization

C28H4 sterically hindered molecular solid

properties of solid/molecule C60 C28H4

lattice constant 13.9 16.3

conduction bands DOS (eV/spin/molecule) 8--10 4--5

binding energy (eV/molecule) 0.6 0.2

LUMO-HOMO gap (eV) 1.6 2

Vep (meV) [Intramolecular phonons only] 64 169

Ab initio calculations performed within DFT-LDA using SIESTA.

Hyperdiamond (HD) solids are diamond lattices with fullerene(tetrahedral symmetry) as a basis.

Schematic diagrams of the 1st nearest-neighbor (n.n.) in the HD structures (top) with examples of pairs of C

28-derived molecules

shown below. The lattice sites in the solid are highlighted by the grey spheres enclosed in the tetrahedra. The two distinct orientations of the constituent molecules are represent by those of the tetrahedra. The n.n. pairs show two distinct bonding configurations: (a) apex-bonded C

28 HD forms covalent

bonds† (b) face-bonded C

28H

4 HD forms weak bonds

†E. Kaxiras et. al, Phys. Rev. B 49, 8446 (1994).

(a) For the C60

solid, the set of three

(five) bands above (below) the gap are derived from the three (five)-fold degenerate LUMO (HOMO) of the C

60

molecule. (b) For the C

28H

4 solid, the set of six

bands above and below the gap are derived respectively from the three-fold degenerate LUMO and HOMO for each C

28H

4 in the two-molecule

cell.

Similarities include: weakly broadened bands & large band gaps.NOTE: Units of DOS (states/eV/spin/cell)

Band structure comparison among three doping scenarios:(a) Intercalation of Na atoms into tetrahedral site(b) Intercalation of Na atoms into interstitial site between opposing six-membered rings on n.n. C

28H

4

(c) Encapsulation of Na atom into the C28

H4 cage

Legend: Solid C28

H4 bands;

Dopant bands; Femi Level.

(a) Sodium and Hydrogen s states hybridize lead to dopant bands at Fermi level.(b) Lattice constant increases from 16.3 Ang. to 18.1 Ang; Jahn-Teller Effect in C

28H

4

-

leads to a gap opening in the solid.(c) Ideal doping case → rigid band donor

The superconducting transition temperature Tc can be estimated

using McMillan's solution to the Eliashberg Equations:

1. µ∗ ≈ 0.22 (for C60

and C28

H4)

2. ωln

≈ 1000 K (for C60

and C28

H4)

3. λ (Na@C28

H4) ≈ 1.5λ (K

3C

60)

4. Tc(K

3C

60) = 19.3 K leads to λ (K

3C

60) = 0.84

5. Tc(Na@C

28H

4) ≈ 3T

c(K

3C

60) ≈ 58 K

Estimated Tc for Na@C

28H

4 is higher than that of Cs

3C

60 (40 K).

T c=ln

1.2exp [− 1

−*10.62 ]

1. C28

H4 forms a molecular solid similar to C

60.

2. Conventional doping of alkali atoms into interstitial sites in C

28H

4 solids is problematic.

3. Endohedrally doped C28

H4 may superconduct with T

c ≈ 58 K.

* Results published in PRB 70, 140504(R) (2004).

AcknowledgmentsThis work funded by NSF DMR-99-76650, DMR-03-25939 and DOE DEFG-96-ER45439.Calculations performed on NCSA IBM p690, the PSC Alphaserver & MCC IBM.

Conclusions

C28

-derived Molecular Solids: Structure, Doping & Electron-Phonon Interaction

Nichols A. Romero, Jeongnim Kim, and Richard M. Martin Department of Physics, Materials Research Laboratory and

Materials Computation Center, University of Illinois, Urbana, IL 61801

Isocharge density surface for (Left) apex-bonded C28

HD and (Right) face-bonded C

28H

4 HD. Notice the lack of bonds in the

molecular solid C28

H4.